Bayesian Inference for Nonnegative Matrix Factorisation Models | Zendy

Ali Taylan Cemgil | Zendy

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Bayesian Inference for Nonnegative Matrix Factorisation Models

Author(s) -

Ali Taylan Cemgil

Publication year - 2009

Publication title -

computational intelligence and neuroscience

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.605

H-Index - 52

eISSN - 1687-5273

pISSN - 1687-5265

DOI - 10.1155/2009/785152

Subject(s) - non negative matrix factorization , model selection , bayesian inference , computer science , bayesian probability , monotonic function , bayes' theorem , inference , statistical inference , artificial intelligence , generative model , pattern recognition (psychology) , algorithm , mathematics , matrix decomposition , statistics , generative grammar , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics

We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction.

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